2.1.1.A Truth Tables & Logic Expressions
Activity 2.1.1 AOI Design: Truth Tables to Logic ExpressionsIntroductionThe first step in designing a new product is clearly defining the design requirements or design specifications. These design specifications detail all of the features and limitations of the product.1.MNF10010101001112.XYF2001010101111F1 = F2 = 3.PQRF3000000110100011010011010110111104.JKLF400000011010001111001101011001111F3 =F4 =In digital electronics, the process of translating these design specifications into a functioning circuit starts with the creation of a truth table. A truth table is simply a list of all possible binary input combinations that could be applied to a circuit and the corresponding binary outputs that the circuit produces. Once the truth table is complete, a Boolean expression can easily be written directly from the truth table. In this activity you will learn how to translate design specifications into truth tables and, in turn, write un-simplified logic expressions from these truth tables.Truth Tables to Logic Expressions: Write the un-simplified logic expression for each of the following truth tables. Logic Expressions to Truth Tables Now that you have mastered the process of writing an un-simplified logic expression from a completed truth table, let’s reverse the process. For the following logic expressions, create a corresponding truth table. Note that some terms in the logic expression may map to more than one place in the truth table. QUOTE Fa=C D + C D QUOTE Fb=R S T + R S T + R S T +R S T Seat Belt Alarm CircuitNow that you understand the mechanics of converting from a truth table to a logic expression (and vice-versa), let’s look at a circuit design problem. Your new car has an audio alarm that buzzes whenever the door is open and the key is in the ignition or when the key is in the ignition and the seatbelt is not buckled. Complete the truth table shown below that captures the functionality of this audio alarm.Use the following variable names and assignment conditions:D: Door → 0=Door Open / 1=Door Close K: Key → 0=Key Not in Ignition / 1=Key in IgnitionS: Seat → 0=Not Buckled / 1=BuckledB: Buzzer → 0=Buzzer Off / 1=Buzzer On1028701841500DKSB(Door)(Key)(Seat Belt)(Buzzer)000001010011100101110111Using the truth table you just completed, write the un-simplified logic expression for the buzzer. Be sure that your answer is in the Sum-of-Products form.Note: Some of you may have been able to extract this simplified logic expression directly from the specifications. If so, you may be asking yourself, why did I have to go through the process of creating the truth table and writing the un-simplified logic expression first? This was a simple problem. As you progress through this class, the design problems will become more difficult The process that you are learning now will become invaluable in solving more challenging problems.Humidity Sensor CircuitYour Aunt Mary would like you to design a digital logic circuit that monitors the conditions in a room of her house where her seven cats live. The room’s temperature is monitored by a temperature sensor. The room’s humidity is monitored by a humidity sensor. The air quality of the room is monitored by a special sensor that measures air particle density. The three sensors output a one (1) to indicate an out-of-range condition. Located outside of the room is an ALERT light that is on (1) whenever two or more sensors are out-of-range.95259461500Create a truth table that captures the functionality of this room monitoring system. Using the truth table that you just created, write the un-simplified logic expression for the ALERT light. Be sure that your answer is in the Sum-of-Products form. ................
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